Greatest Common Factor of 960 and 1800
GCF(960, 1800) = 120, Greatest common factor of 960 and 1800 is 120. Greatest Common Factor or Greatest Common Divisor of two numbers is the largest integer by which both the numbers can be divided. There are two different methods to calculate Greatest Common Factor of 960 and 1800. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 960 and 1800 by prime factorization method
We will first find the prime factorization of 960 and 1800.
Prime Factorization of 960 is 1, 2, 2, 2, 2, 2, 2, 3, 5 and Prime Factorization of 1800 is 1, 2, 2, 2, 3, 3, 5, 5.
- Factorize\( (960) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 5\)
- Factorize\( (1800) = \) \(1\times 2\times 2\times 2\times 3\times 3\times 5\times 5\)
Now we need to find any which are common for each number (1, 2, 2, 2, 3, 5) and multiply these numbers together.
\(GCF(960, 1800) = 1\times 2\times 2\times 2\times 3\times 5 = 120\).
Greatest Common Factor of 960 and 1800 by matching factors method
List of positive integers factors of 960 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
List of positive integers factors of 1800 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800
As you can see, 120 is the greatest and common number that 960 and 1800 divides into.
So the greatest common factor 960 and 1800 is 120.
\(GCF(960, 1800) = 120\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
